Increases in Risk and the Demand for Insurance

Many people anticipate that a risk-averse agent faced with an exogenous mean preserving increase in risk will take a less risky position or will demand more insurance. This widespread belief does not always turn out to be true in the insurance market and, more generally, in many other economic examples. This negative result has prompted many theoretical investigations to obtain intuitively acceptable results. Some authors have searched for conditions on the utility function, others have presented subclasses of mean preserving increases in risk, while a third group has considered the two kinds of restrictions jointly. It is interesting to notice that none of these contributors have applied their analysis to the insurance problem, although Meyer and Ormiston (1989) have interpreted the nature of insurance contracts as simple risk-reducing transformations. The object of this article is to fill this gap in literature. By examining the study of the coinsurance coverage, we show that one of its specifications, namely the linearity of the payoff in the decision variable and in the random element, does not preclude the applicability of well-known theorems to the demand for insurance.